Greg is right. Khatas are an offering. Used to be that khatas were only returned to the giver as a mark of special blessing and appreciation. Now, Lamas routinely give back khatas. Otherwise, what to do with all the khatas? However, sometimes khatas are kept as special sign of appreciation. For instance, a couple of months ago I arranged a Medicine Buddha lung at Shechen Monastery in Boudha for a bunch of medical volunteers. Everyone got their khata back from the Khenpo. I was the last person to offer a khata and the Khenpo kept it as a tendrel since I was the one who arranged for the event. When a khata is returned to the giver, it is a blessing. But offering the khata is an offering; it's not meant as something to be blessed and returned to the offerer.

Back in the old days, when most khatas were kept, the Lama's treasurer would later resell the khatas as a way of making money for the labrang. Used to be that, after a large event, there would be a mountain of khatas in front of the Lama's table/throne.